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Motzkin proves that $f(n)\to\infty$: $n$ points in the real plane, not all on one line, determine a number of ordinary lines (lines through exactly two of the points) that grows without bound with $n$. His lower bound is of order $\sqrt n$, as the Kelly-Moser source card records when it compares the later bounds with his. This answers the first question of Problem 210; the Sylvester-Gallai theorem, which the paper also discusses, gives only $f(n)\ge 1$.

Covers. The first question, whether $f(n)\to\infty$, with a lower bound of order $\sqrt n$. It does not give a linear bound and does not determine how fast $f(n)$ grows, which the later claims settle.

The result is refereed: Th. Motzkin, The lines and planes connecting the points of a finite set, Trans. Amer. Math. Soc. 70 (1951), no. 3, 451-464. The site's page credits this paper with $f(n)\to\infty$, the answer to the first question; its label, proved, covers both questions and rests for the second on the later results, so the acceptance here stands on the refereed publication.